There is an easy fix for all of this.
Rule 1. Each division winner gets into the playoffs, except when a division cannot field a winner that has won at least 8 games. In this case the vacated playoff spot would go to the next team with the best record unless the next best record not in the playoffs doesn't have at least 8 wins, then the playoff spot goes back to the division winner.
2. All playoff seeding will be done by records. If you have the second best record in the conference you will have the second seed, even if the best record was in your division. The higher seed will always host the playoff game.
3 tie breakers will be the same as always except the second tie breaker will be division winners. So head to head first, then division winner, then however it is now.
4. Teams can make the playoffs with a losing record, but only if the are one of the top 6 teams or however large the field is.
5. Losing teams can host a playoff game, if and only if the team they are playing has a worse record or the same record and they own the tiebreakers.
All these rules would ensure that the division rivalries stay intact, while the best teams are the teams with a chance to go to the Super Bowl. It also rewards the best teams with home games and rewards division winners with a playoff berth, but doesn't reward average or poor division winners a second reward with a playoff berth and home game.